Orthogonal frequency division multiplexing (OFDM) is a modulation method used in traditional, high-speed wireless networks. However, waveforms generated using traditional OFDM techniques exhibit noise-like properties, and thus OFDM waveforms tend to suffer from relatively large peak-to-average ratios (PARs), which in turn may lead to significant distortion noise and low power efficiency in peak-limited channels. In addition, under relatively harsh channel conditions, transmitted OFDM signals tend to incur significant timing offsets and carrier frequency offsets. Because traditional OFDM techniques tend not to be robust under harsh channel conditions, significant timing offsets may result in inter-block interference, and significant carrier frequency offsets may result in inter-carrier interference. Both of these forms of interference are detrimental to the bit error rates of received signals.
In order to estimate the channel and to address timing and carrier frequency offsets, some traditional OFDM devices transmit a preamble in conjunction with and preceding an information-bearing OFDM sequence. The receiver may perform a conjugate correlation of the received preamble and an expected preamble to determine estimates for the timing and carrier frequency offsets. In addition, when the preamble also includes channel training information, the preamble also may be used to perform channel estimation. Although transmission of a preamble is relatively simple to implement, a tradeoff to implementing this technique is that a significant amount of bandwidth is used solely for preamble transmission, and thus for synchronization, acquisition, and, when channel training information is available, also for channel estimation.
In addition, the channel estimate naturally has some error, when compared with actual channel conditions. Traditional OFDM transmission methods may experience an increase in channel estimation errors on the receiver side, which may result from non-linear amplification, by a power amplifier device on the transmitter side, of transmit information sequences having higher than desired PARs. Such non-linear transmission may cause significant out-of-band interference (i.e., interference outside the signal bandwidth, such as in the adjacent channels and/or other user channels), and also may induce undesired in-band interference, which adds distortion the transmitted information bits and also to the channel training information. Furthermore, improper synthesis of the channel training information may lead to further channel estimation errors at the receiver. Thus, non-linear amplification of high peak-to-average power ratio signals and improper channel training information design may, in the receiver, result in unacceptably high channel estimation errors and excessively high bit error rates.
In some OFDM systems, prior to transmission, an information-bearing OFDM sequence is combined with a synchronization/pilot sequence, which provides spectral efficiency improvements over preamble-based synchronization approaches. Traditional sequences include, for example, Pseudorandom Number (PN) sequences, Gold codes, Kasami codes, and m-sequences. Although traditional synchronization/pilot sequences are appropriate for some situations, they do not provide for adequate system performance in other situations. For example, although traditional sequences are designed to perform relatively well for synchronization purposes, they are not designed to provide low PAR or flat frequency response in conjunction with optimal channel estimation by the receiver. Essentially, in an OFDM system, traditional synchronization/pilot sequences do not provide for adequate system performance in channel environments in which significant timing offsets, carrier frequency offsets, and multi-path fading effects simultaneously are present.
Accordingly, what are needed are methods and apparatus for generating synchronization/pilot sequences that provide for adequate system performance even under harsh channel conditions, and methods and apparatus for generating and transmitting OFDM waveforms in which these synchronization/pilot sequences are embedded. More particularly, what are needed are methods and apparatus for generating synchronization/pilot sequences that have synchronization properties that are at least as good as the synchronization properties of traditional sequences, and that also exhibit low-PAR properties and a flat frequency response. Other features and characteristics of the inventive subject matter will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and this background.